The "Tsiolkovsky equation" is the fundamental equation for spacecraft launch. It is used to describe the motion of vehicles that follow the basic principle of rocket: based on the principle of conservation of momentum, any device, through a propulsion system that consumes its mass in the opposite direction, can generate and obtain acceleration on its original speed.In this case, I want to use an expansion of "Tsiokovsky equation" to simulate the trajectory of Falcon 9 rocket.

However, the general "Tsiolkovsky equation" is an extremely ideal speculation that assumes the external force on the rocket is 0 without gravity and air resistance.Therefore, this page is going explore the revised Tsiolkovsky equation considering gravity and air resistance. Before exploring the motion equation of the rocket, we must first establish the conservation of momentum formula under the rocket system.